Finite Group Databasebeta

← C2×#10591346 #11808193

Subgroups — C2×#10591346 #11808193

Order 1152.

2025 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×Dic6C211yesmaximal, characteristic
2C22×#3750C211yesmaximal, characteristic
3C22×Dic3⋊Dic3C212yesmaximal
4C2×C3×C3⋊#95C211yesmaximal, characteristic
5C2×#63579C212yesmaximal
6#10591346C218yesmaximal, direct product factor
7C2×#5230—31nomaximal
8C2×#4656—31nomaximal
9C23×C32×C4C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C23×C3×Dic3C2212yes—
13C23×C3×Dic3C2212yes—
14C22×C3×Dic6—24no—
15C22×C3×Dic6—28no—
16C22×C3×Dic6C2214yes—
17C2×#3750—24no—
18C2×#3750C2214yes—
19C2×Dic3⋊Dic3—28no—
20C2×Dic3⋊Dic3C2218yes—
21C3×C3⋊#95C2214yes—
22#63579C2218yes—
23C23×C3×Q8—31no—
24C23×Dic6D311yescharacteristic
25C22×C4⋊Dic3—32no—
26C22×Dic3⋊C4—31no—
27C22×Dic3⋊C4—31no—
28C22×Dic3⋊C4—32no—
29C22×Dic3⋊C4—61no—
30C2×C3×#95—31no—
31#5230—38no—
32C2×C3⋊#95—32no—
33C2×C3⋊#95—32no—
34C2×C3⋊#95D311yescharacteristic
35#4656—38no—
36C24×C32C2311yescharacteristic
37C22×C32×C4—24no—
38C22×C32×C4D414yes—
39C22×C32×C4C2312yes—
40C22×C3⋊Dic3—22no—
41C22×C3⋊Dic3—22no—
42C22×C3⋊Dic3—22no—
43C22×C3⋊Dic3—24no—
44C22×C3⋊Dic3Q814yescomplemented
45C22×C3⋊Dic3C2312yes—
46C22×C3⋊Dic3C2312yes—
47C22×C3×Dic3—24no—
48C22×C3×Dic3—24no—
49C22×C3×Dic3—24no—
50C22×C3×Dic3—24no—
51C22×C3×Dic3D418yes—
52C22×C3×Dic3Q818yescomplemented
53C22×C3×Dic3C2314yes—
54C22×C3×Dic3C2314yes—
55C2×C3×Dic6—232no—
56C2×C3×Dic6—28no—
57C2×C3×Dic6—216no—
58#3750—28no—
59Dic3⋊Dic3—216no—
60C2×#395—91noSylow
61C22×C3×Q8—34no—
62C22×C3×Q8—68no—
63C22×C3×Q8—64no—
64C23×C3×C4—21no—
65C23×C3×C4—32no—
66C23×C3×C4—32no—
67C23×C3×C4C2×D311yescharacteristic
68C23×C3×C4C2×D311yescharacteristic
69C23×Dic3—31no—
70C23×Dic3—31no—
71C23×Dic3—31no—
72C23×Dic3—31no—
73C23×Dic3—61no—
74C23×Dic3—61no—
75C23×Dic3C2×D312yes—
76C23×Dic3C2×D312yes—
77C22×Dic6—24no—
78C22×Dic6—28no—
79C22×Dic6C2×D314yes—
80C2×C4⋊Dic3—38no—
81C2×C4⋊Dic3—68no—
82C2×Dic3⋊C4—34no—
83C2×Dic3⋊C4—34no—
84C2×Dic3⋊C4—38no—
85C2×Dic3⋊C4—64no—
86C2×Dic3⋊C4—68no—
87C2×Dic3⋊C4—68no—
88C2×Dic3⋊C4—64no—
89C2×Dic3⋊C4—64no—
90C3×#95—34no—
91C3⋊#95—38no—
92C3⋊#95—38no—
93C3⋊#95C2×D314yes—
94C23×C32C2×D412yes—
95C23×C32C2×D414yes—
96C23×C32C2×Q814yes—
97C23×C32C2×Q812yes—
98C23×C32#4112yes—
99C23×C32C2411yescharacteristic
100C2×C32×C4—28no—
101C2×C32×C4—24no—
102C2×C32×C4C2×D414yes—
103C2×C3⋊Dic3—28no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3—24no—
108C2×C3⋊Dic3—44no—
109C2×C3⋊Dic3C2×Q814yescomplemented
110C2×C3×Dic3—216no—
111C2×C3×Dic3—216no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3C2×D418yes—
117C2×C3×Dic3C2×Q818yescomplemented
118C3×Dic6—232no—
119C23×Q8—31no—
120C22×C4⋊C4—92no—
121C22×C4⋊C4—91no—
122#395—98no—
123C2×#95—31no—
124C2×#95—92no—
125C24×C3—21no—
126C24×C3C22×D311yescharacteristic
127C24×C3C22×D311yescharacteristic
128C2×C3×Q8—616no—
129C2×C3×Q8—632no—
130C2×C3×Q8—68no—
131C22×C3×C4—24no—
132C22×C3×C4—24no—
133C22×C3×C4—24no—
134C22×C3×C4—22no—
135C22×C3×C4—38no—
136C22×C3×C4—38no—
137C22×C3×C4—34no—
138C22×C3×C4—34no—
139C22×C3×C4—44no—
140C22×C3×C4—64no—
141C22×C3×C4—64no—
142C22×C3×C4—64no—
143C22×C3×C4—64no—
144C22×C3×C4D1214yes—
145C22×C3×C4#6714yes—
146C22×C3×C4C22×D312yes—
147C22×C3×C4C22×D312yes—
148C22×Dic3—24no—
149C22×Dic3—24no—
150C22×Dic3—24no—
151C22×Dic3—24no—
152C22×Dic3—34no—
153C22×Dic3—34no—
154C22×Dic3—32no—
155C22×Dic3—32no—
156C22×Dic3—32no—
157C22×Dic3—32no—
158C22×Dic3—62no—
159C22×Dic3—64no—
160C22×Dic3—62no—
161C22×Dic3—64no—
162C22×Dic3—64no—
163C22×Dic3—62no—
164C22×Dic3—62no—
165C22×Dic3—62no—
166C22×Dic3—62no—
167C22×Dic3—64no—
168C22×Dic3—62no—
169C22×Dic3—64no—
170C22×Dic3—62no—
171C22×Dic3—64no—
172C22×Dic3—124no—
173C22×Dic3Dic618yescomplemented
174C22×Dic3#6718yes—
175C22×Dic3C22×D314yes—
176C22×Dic3C22×D314yes—
177C2×Dic6—232no—
178C2×Dic6—28no—
179C2×Dic6—216no—
180C4⋊Dic3—616no—
181Dic3⋊C4—616no—
182Dic3⋊C4—616no—
183Dic3⋊C4—68no—
184Dic3⋊C4—68no—
185C22×C32#12014yes—
186C22×C32C22⋊Q818yes—
187C22×C32C22⋊Q814yes—
188C22×C32C4⋊Q814yes—
189C22×C32C4⋊Q818yes—
190C22×C32C22×D411yescharacteristic
191C22×C32C22×D412yes—
192C22×C32C22×Q812yes—
193C22×C32C22×Q811yescharacteristic
194C22×C32C2×#4111yescharacteristic
195C32×C4—24no—
196C3⋊Dic3—24no—
197C3⋊Dic3—42no—
198C3×Dic3—28no—
199C3×Dic3—28no—
200C22×Q8—34no—
201C22×Q8—68no—
202C22×Q8—64no—
203C23×C4—32no—
204C23×C4—32no—
205C23×C4—91no—
206C23×C4—91no—
207C23×C4D3211yescharacteristic
208C2×C4⋊C4—98no—
209C2×C4⋊C4—94no—
210C2×C4⋊C4—188no—
211C2×C4⋊C4—184no—
212#95—34no—
213#95—98no—
214C23×C3—21no—
215C23×C3—24no—
216C23×C3—22no—
217C23×C3—22no—
218C23×C3—22no—
219C23×C3—24no—
220C23×C3C2×Dic614yes—
221C23×C3C2×D1212yes—
222C23×C3D3×D414yes—
223C23×C3#23712yes—
224C23×C3D3×Q814yes—
225C23×C3D3×Q812yes—
226C23×C3D3×Q812yes—
227C23×C3#23912yes—
228C23×C3C2×#6712yes—
229C23×C3C2×#6714yes—
230C23×C3C23×D311yescharacteristic
231C23×C3C23×D311yescharacteristic
232C3×Q8—632no—
233C2×C3×C4—28no—
234C2×C3×C4—28no—
235C2×C3×C4—24no—
236C2×C3×C4—24no—
237C2×C3×C4—24no—
238C2×C3×C4—38no—
239C2×C3×C4—38no—
240C2×C3×C4—44no—
241C2×C3×C4—48no—
242C2×C3×C4—616no—
243C2×C3×C4—616no—
244C2×C3×C4—64no—
245C2×C3×C4—64no—
246C2×C3×C4—64no—
247C2×C3×C4—64no—
248C2×C3×C4C2×D1214yes—
249C2×C3×C4C2×#6714yes—
250C2×Dic3—216no—
251C2×Dic3—216no—
252C2×Dic3—24no—
253C2×Dic3—24no—
254C2×Dic3—24no—
255C2×Dic3—24no—
256C2×Dic3—34no—
257C2×Dic3—34no—
258C2×Dic3—64no—
259C2×Dic3—64no—
260C2×Dic3—64no—
261C2×Dic3—616no—
262C2×Dic3—68no—
263C2×Dic3—68no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—62no—
268C2×Dic3—64no—
269C2×Dic3—62no—
270C2×Dic3—64no—
271C2×Dic3—62no—
272C2×Dic3—64no—
273C2×Dic3—124no—
274C2×Dic3—128no—
275C2×Dic3—124no—
276C2×Dic3—124no—
277C2×Dic3C2×Dic618yescomplemented
278C2×Dic3C2×#6718yes—
279Dic6—232no—
280C2×C32#39518yescomplemented
281C2×C32C2×#12011yescharacteristic
282C2×C32C2×C22⋊Q812yes—
283C2×C32C2×C22⋊Q811yescharacteristic
284C2×C32C2×C4⋊Q811yescharacteristic
285C2×C32C2×C4⋊Q812yes—
286C24C2×D3211yescharacteristic
287C2×Q8—616no—
288C2×Q8—632no—
289C2×Q8—68no—
290C22×C4—24no—
291C22×C4—34no—
292C22×C4—34no—
293C22×C4—38no—
294C22×C4—38no—
295C22×C4—64no—
296C22×C4—64no—
297C22×C4—64no—
298C22×C4—64no—
299C22×C4—92no—
300C22×C4—94no—
301C22×C4—92no—
302C22×C4—182no—
303C22×C4—182no—
304C22×C4—182no—
305C22×C4—184no—
306C22×C4#62614yes—
307C22×C4C2×D3212yes—
308C4⋊C4—1816no—
309C4⋊C4—188no—
310C22×C3—22no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—22no—
315C22×C3—28no—
316C22×C3—24no—
317C22×C3—24no—
318C22×C3—28no—
319C22×C3—24no—
320C22×C3#86914yes—
321C22×C3#87818yes—
322C22×C3#88214yes—
323C22×C3#88818yes—
324C22×C3#89714yes—
325C22×C3#94418yes—
326C22×C3#94414yes—
327C22×C3#94614yes—
328C22×C3#94618yes—
329C22×C3#95314yes—
330C22×C3C22×Dic612yes—
331C22×C3C22×D1211yescharacteristic
332C22×C3C2×D3×D412yes—
333C22×C3C2×#23711yescharacteristic
334C22×C3C2×D3×Q812yes—
335C22×C3C2×D3×Q811yescharacteristic
336C22×C3C2×D3×Q811yescharacteristic
337C22×C3C2×#23911yescharacteristic
338C22×C3C22×#6711yescharacteristic
339C22×C3C22×#6712yes—
340C3×C4—24no—
341C3×C4—24no—
342C3×C4—44no—
343C3×C4—68no—
344C3×C4—68no—
345Dic3—28no—
346Dic3—28no—
347Dic3—68no—
348Dic3—64no—
349Dic3—64no—
350Dic3—124no—
351Dic3—122no—
352Dic3—122no—
353C32C2×#39511yescharacteristic, complemented, Sylow
354C23D3×Dic614yes—
355C23#379612yes—
356C23#379712yes—
357C23C2×#62612yes—
358C23D3×#6714yes—
359C23C22×D3211yescharacteristic
360Q8—632no—
361C2×C4—24no—
362C2×C4—28no—
363C2×C4—38no—
364C2×C4—38no—
365C2×C4—64no—
366C2×C4—64no—
367C2×C4—64no—
368C2×C4—64no—
369C2×C4—616no—
370C2×C4—616no—
371C2×C4—94no—
372C2×C4—182no—
373C2×C4—182no—
374C2×C4—188no—
375C2×C4—182no—
376C2×C4—184no—
377C2×C4—364no—
378C2×C4C2×#62614yes—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—22no—
382C2×C3—28no—
383C2×C3—21no—
384C2×C3—22no—
385C2×C3#465618yescomplemented
386C2×C3#523018yescomplemented
387C2×C3C2×#86911yescharacteristic
388C2×C3C2×#87812yes—
389C2×C3C2×#88211yescharacteristic
390C2×C3C2×#88812yes—
391C2×C3C2×#89711yescharacteristic
392C2×C3C2×#94411yescharacteristic
393C2×C3C2×#94412yes—
394C2×C3C2×#94611yescharacteristic
395C2×C3C2×#94612yes—
396C2×C3C2×#95311yescharacteristic
397C22#6383918yes—
398C22#6386614yes—
399C22#6387114yes—
400C22#6388718yes—
401C22#6397714yes—
402C22C2×D3×Dic612yes—
403C22C2×#379611yescharacteristic
404C22C2×#379711yescharacteristic
405C22C22×#62611yescharacteristic
406C22C2×D3×#6712yes—
407C4—24no—
408C4—68no—
409C4—68no—
410C4—184no—
411C4—362no—
412C3—21no—
413C3C2×#465611yescharacteristic, complemented
414C3C2×#523011yescharacteristic, complemented
415C2#1059134618yesdirect product factor
416C2C2×#6383912yes—
417C2C2×#6386611yescharacteristic
418C2C2×#6387111yescharacteristic
419C2C2×#6388712yes—
420C2C2×#6397711yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32C2×#395
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
6. #10591346C2direct (N × H)
44. C22×C3⋊Dic3Q8semidirect
52. C22×C3×Dic3Q8semidirect
109. C2×C3⋊Dic3C2×Q8semidirect
117. C2×C3×Dic3C2×Q8semidirect
173. C22×Dic3Dic6semidirect
277. C2×Dic3C2×Dic6semidirect
280. C2×C32#395semidirect
353. C32C2×#395semidirect
385. C2×C3#4656semidirect
386. C2×C3#5230semidirect
413. C3C2×#4656semidirect
414. C3C2×#5230semidirect
415. C2#10591346direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×C3×Dic62
C22×#37502
C22×Dic3⋊Dic32
C2×C3×C3⋊#952
C2×#635792
#105913462
C2×#52303
C2×#46563